Solution
For pair 1
[tex]\begin{gathered} f(x)=2x-6,g(x)=\frac{x}{2}+3 \\ \mathrm{A\: function\: g\: is\: the\: inverse\: of\: function\: f\: if\: for}\: y=f\mleft(x\mright),\: \: x=g\mleft(y\mright)\: \end{gathered}[/tex][tex]\begin{gathered} f(x)=2x-6 \\ f(x)=y \\ y=2x-6 \\ x=2y-6 \\ x+6=2y \\ \text{divide both side by 2} \\ \frac{x+6}{2}=\frac{2y}{2}_{} \\ y=\frac{x}{2}+3 \end{gathered}[/tex]
They are inverse of each other
For pair 2
[tex]\begin{gathered} f(x)=7x,g(x)=-7x \\ \text{Inverse of f(x) = x/7} \end{gathered}[/tex][tex]\begin{gathered} f(x)=7x \\ y=7x \\ x=7y \\ y=\frac{x}{7} \end{gathered}[/tex]
They are not inverse of each other
Therefore only pair 1 are inverse of each other
Hence the correct answer is Option B
